MIT mathematicians model traffic jams like detonation waves

Most drivers have been stuck in a traffic jam at one point or another. Some of the jams are caused by an accident or closed lanes. Other traffic jams crop up with seemingly no reason.

A group of mathematicians at MIT is working on the development of a new model to explain how and why these so-call phantom traffic jams form. According to the researchers, these types of phantom traffic jams form when there are a lot of cars on the road and small disturbances like a driver hitting the brakes too hard or getting too close to another car. These little disturbances can escalate into a self-sustaining traffic jam.

The model developed by the team of researchers may help road designers build roads to minimize the possibility of phantom traffic jams. The key to the study is the discovery that the mathematics of these jams called jamitons are very similar to the equations used to describe the detonation waves produced by explosions.

The discovery of the jamitons allowed the researchers to solve traffic jam equations first theorized in the 1950's. The equations are reportedly similar to those used in fluid mechanics and model traffic jams as self-sustaining waves. The equations allowed the researchers to calculate the conditions that case a jamitons to form and how fast the jamiton will spread.

According to the researchers, once this type of jamiton forms it is nearly impossible to break up and a driver’s only choice is to wait the jamiton out. The researchers say that the new model can help road designers to determine speed limits that are safer and find stretches of road where accidents are more likely.

One of the researchers, Aslan Kasimov, said, "We wanted to describe this using a mathematical model similar to that of fluid flow." Kasimov and his team say that they discovered that jamitons have a sonic point that separates traffic flow into upstream and downstream components. Communication of the cause of the jamiton to drivers it the downstream segment of traffic is impossible say the researchers.

There is a way to measure distance in time units and this can be found in some safety guidances. Theoretically if all cars keep distance considered safe (3 seconds to the next car) the distance will be proportional to speed and highway throughput will stay the same at any non-zero speed. But, that is only if we don't count car length. Safe distance between cars increases with the speed but cars don't elongate. So the throughput should increase with the speed unless drivers increase safe distance measured in time units (which is probably the case).

On the side note, people just don't seem to use gas pedal here, in North California. I see a lot when people enter highways at 45-50 mph where limit is 65 mph, and these are not grandmas, these are otherwise normal-looking young and middle-aged men. Maybe they are trying to save on gas that way? And then "inverse race" starts with some car in right lane. The car on highway which is already well below speed limit slows down trying to yield to entering car. And the entering car slows down trying to yield to the car on highway. At around 40 mph they finally settle this desperately slowing down all right lane. And all that when highway is not crowded, there is a lot of room to merge into it. Many people just can't estimate at what point they need to merge and they think the slower the safer.

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